nLab
UC Riverside Seminar on Cobordism and Topological Field Theories

In the last quarter of 2009, there is a seminar at UC Riverside on Cobordism and Topological Field Theories run by Julie Bergner. The seminar webpage is here. The goal is to work through recent notes of Lurie giving an outline of his proof of the Cobordism Hypothesis, relating cobordism classes of manifolds and topological field theories. This work brings together several areas of recent mathematical interest: topological field theories, cobordisms of manifolds, and homotopical approaches to higher categories. The basic definitions and examples of all of the above will be covered and then we’ll work towards understanding Lurie’s proof.

Friday, September 25 — John Baez, Introduction to the cobordism hypothesis

John Baez kicked off the seminar with an introduction to the cobordism hypothesis, how it began its life, and what it means in dimension n=1n=1. Already here an issue of “framing” comes into play concerning the first Reidemeister move.

Friday, October 23 — John Huerta, A short history of the interaction between quantum field theory and topology

Today’s story should involve lots of people, but the stars are Sir Michael Atiyah and Edward Witten. It begins with a paper Witten wrote in 1982, called “Supersymmetry and Morse Theory”. In this paper, Witten shows how to use ‘supersymmetric quantum mechanics’ to compute the de Rham cohomology of a compact manifold, MM, via Morse theory. This was perhaps the first instance of using quantum theory to find topological invariants.